The present invention is generally directed to a method and apparatus for the determination of the modulation transfer function of optical systems and, more particularly, by using a deflectometric moire fringe pattern.
The MTF is a quantitative measure of image quality. It describes the ability of an optical system as a function of spatial frequency to transfer the contrast of an object to the image. The MTF data, together with the focal number and physical dimensions of an optical element, provide a comprehensive description of the expected performance, and as such, are indispensable in optical design of multi-components imaging systems. The MTF concept is also most useful in defining the degradation of image quality caused by turbulent atmosphere. The turbulence of the atmosphere has a detrimental effect on air reconnaissance, outdoor photography, and in general, whenever a telescopic camera is used.
MTF is nowadays considered far superior to any of the classical resolution criteria, which only set an upper bound to the spatial frequency which can be resolved. MTF, on the other hand, provides the system's response over practically the entire spectrum of spatial frequencies. Therefore, MTF determination has become a routine test of optical products, and MTF data is supplied by the manufacturers of high performance optical equipment.
Prior art methods for MTF determination can be divided into two categories. They are direct measurements and indirect measurements of MTF. The first approach is based on the use of test target, usually linear gratings, as the object in the tested optical system. The contrast of the image formed by the system is compared to that of the original object. The ratio provides the required MTF at the grating's frequency. A full MTF curve is obtained by scanning with a series of such gratings, to cover the desired spectral range of spatial frequencies. This method is clearly cumbersome, since it involves repeated scanning with a whole series of gratings of respectively differing spatial frequencies. Furthermore, although the MTF concept is defined and, hence, the measurement is accurate only for sine wave gratings, because of the difficulties in producing high quality sine wave gratings, usually bar-test charts, known as square wave gratings, which are easier to manufacture, are employed. Therefore, the derived MTF curves, measured with square wave gratings, deviate from the theoretical value.
The indirect approach of deriving MTF curves is based on Fourier analysis of the line spread function, obtained by a narrow slit, preceding the tested system. This technique requires elaborate computation, and is therefor far less popular.